One of Greta Gerwig's favourite stories is about the time the young Marlon Brando first walked on stage, apparently looking so natural some of the audience assumed he was a stagehand or some guy off the street who'd just wandered up there accidentally. "People thought, 'What's happening? Is that acting?'" she says. "Not that I'm comparing myself to Marlon Brando but that's so exciting to me."

We've become accustomed to seeing people do things in the movies that we never do in real life, like walking away from explosions without turning around, dancing alone in the street when they get good news, or delivering inspirational speeches off the cuff. We know it's not real. We don't want it to be real. But then an actor comes along who makes everyone else look like they're acting, and the accepted standards of the profession need rejigging. Brando and his method buddies were one such reality check, but we could be witnessing another.

Gerwig has mastered the art of artlessness. Formerly queen of the much-maligned indie movement known as "mumblecore", the 26-year-old Californian is taking her first tentative steps into the mainstream with the film Greenberg, and she doesn't just look comfortable there, she makes everyone else look a little uncomfortable. Greenberg is ostensibly the new Ben Stiller movie, or for indie auteur-spotters the new Noah Baumbach movie, but it's Gerwig who sets the dramatic tone. And Stiller, an actor who usually plays at the rubber-faced end of the subtlety spectrum, is all the better for dialing it down and matching her. "With Greta, you don't feel you're acting; you feel like you're just living real life with her," Stiller says of her. Critics have echoed the sentiment. "Either she's a total natural – most likely – or she has the most invisible technique of any modern actor," said Variety. The New York Times went one better and predicted she "may well be the definitive screen actress of her generation".

Maybe the Brando comparison isn't so far fetched after all. Gerwig plays Florence, bright but spacey assistant to a wealthy Los Angeles family, who's much better at organising everyone else's lives than sorting out her own. You feel like you know someone just like her. "If you worked with her in the office, you'd definitely develop a crush on her, but outside you'd wonder if she was as cute as you thought she was," is how one character describes her. Stiller's character does develop a crush on her, but things play out like a real-life romance, not a movie one, with stilted conversations, false starts, blown opportunities and some excruciatingly bad sex.

"I saw her as a girl whose thighs rubbed together," says Gerwig of her character. "Most people when they get their first big movie, they're told to lose weight and look prettier, but Noah schlumped me up. If you just put on a little bit of weight and don't quite fit into your clothes, you just hold yourself differently and don't feel so great." It's not the most swan-like of Hollywood debuts; more an ugly duckling. Florence is awkward and painfully under-confident. But when you see her drunk and alone in her apartment, dressed in tights and an ill-fitting sweater, singing along to Paul McCartney's dreadful Uncle Albert, your heart goes out to her.

"I think I was really lucky. Noah was really supportive of how I did it," says Gerwig. She's quick to point out that she stuck to Baumbach's script word for word. "He writes in a rhythm, and it's another way of hooking in that makes you feel like you can generate something that looks like spontaneous life."

Things were a little different in Gerwig's mumblecore days. Often there wasn't even a script. As the name suggests, inarticulacy was a defining characteristic of mumblecore, along with hesitancy, self-absorption and a lack of inertia so terminal you couldn't really describe it as a movement at all. Worshipping at the altar of John Cassavetes, and rarely straying beyond their own apartments, this close-knit collective turned out a series of low-budget films that often made viewers want to get up and give the characters a good shake, or a slap, or at least a decent thesaurus. Hannah Takes The Stairs, from 2007, was mumblecore's Breakfast Club. It was directed by key player Joe Swanberg, and starred two other notable directors, Mark Duplass (The Puffy Chair, Baghead) and Andrew Bujalski (Funny Ha Ha, Mutual Appreciation). Gerwig played Hannah, a directionless slightly irritating, post-college hipster, and everyone in the film was in love with her, including the camera. Like all Swanberg's films, it was "written" by the cast as they improvised, but while others look as if they're stumbling, Gerwig seems totally at home. She never studied acting, but she had been involved in college theatre and was set on becoming a playwright before she drifted into film-making.

'Making a film with no money – the way we were doing it – you can really feel quite terrible about yourself and the way your life is going, and feel like nothing will ever work out'

IFC Films/ Everett/Rex

"I don't know, it's quite easy to just slip into," she says. "There wasn't anything specific that was trying to be achieved with those films, as much as just finding what seemed interesting and alive – those moments. In many ways, I was building my parachute on the way down. But you get kind of a hook and you draw the line in. The bad takes are where you're trawling."

Mumblecore was nothing but bad takes to its critics, but they weren't just goofing around. The films were often difficult, draining experiences, Gerwig says. "One of the things about making a film when you have no money and doing it the way we were doing it, you can really feel quite terrible about yourself and about the way your life is going, and feel like nothing will ever work out." This was particularly true of Nights And Weekends, Gerwig and Swanberg's follow-up to Hannah Takes The Stairs, starring themselves as a long-distance couple growing apart. It was never released here but it's both the most frustrating and the most intriguing of the mumblecore movies; at times painfully boring but at others bracingly intense and unbearably intimate. She and Swanberg had an awful, exhausting time making the film, she says. They were never a real-life couple, but they argued and fell out like one, taking a break from each other for nearly year in the middle of it, which kind of fitted the story. When they premiered the film in 2008 at South By Southwest, the Texas film festival that's been mumblecore's spiritual home, Gerwig and Swanberg both looked utterly miserable. "I was," she remembers. "It had taken so much out of me and I was convinced everyone was going to hate it. When I looked at the film, I saw the reality of some of the hard stuff I was going through as a person filtered through this fictional narrative," Gerwig remembers. "Some of those feelings were very real and kind of ugly. I was still having trouble separating it."

You wouldn't exactly call it method acting, but mumblecore nailed something about the social habits of educated but aimless young, white Americans, and it presented its findings unapologetically; a shaky mirror held up to a demographic that would rather be looking at a flattering Facebook profile of itself. As such, it ended up being just the shot of fresh indie realism the mainstream needed.

Noah Baumbach thought so, anyway. He's shaping up to be the conduit between the old and new generations of indiedom, having also been Wes Anderson's writing partner on The Life Aquatic With Steve Zissou and Fantastic Mr Fox, and a director in his own right (The Squid And The Whale, Margot At The Wedding). As well as inviting Gerwig to audition for Greenberg, Baumbach and his wife Jennifer Jason Leigh (who co-developed and stars in the film) cast fellow mumblecore veteran Mark Duplass as one of Stiller's old friends. Duplass has been moving into the mainstream as a director as well. Fox's Searchlight indie division signed him and his brother Jay up, and their latest movie, Cyrus, has a decent budget and recognisable names, like John C Reilly, Jonah Hill, Marisa Tomei and Catherine Keener. In indie cinema terms, that's like landing the cast of Ocean's Eleven. Baumbach also co-produced Joe Swanberg's Alexander The Last, another improv-heavy relationship drama. Swanberg looks to be sticking to his principles, and improving all the time. Andrew Bujalski, too, looks to be staying in mumblecore-ish territory with his Beeswax.

Gerwig, though, seems to have left that life behind her. Despite her onscreen flakiness, she's never lacked ambition. She's currently in Los Angeles shooting Ivan Reitman's next movie – she plays Natalie Portman's best friend. Then she's off to New York to star in Warners' remake of 1981 classic Arthur. After Dudley Moore, it's being retooled as another "you're gonna love this British guy" vehicle, this time for Russell Brand. It's quite a Brit concern all round: the John Gielgud butler role is taken by Helen Mirren, and it's written by the celebrated Peter Baynham, which means Gerwig has been brushing up on Brass Eye and Alan Partridge.

More importantly, she doesn't seem to be daunted, and there are no signs of compromising her hard-won indie credibility. "It feels right, even though it's bigger," she says. Rehearsing and improvising with Brand "felt like playing", she says. Not all that different to what she's always done. "It was, like, 'I know what this is. This is not a big scary Warner Brothers thing. I know how to do this.'"